zggev3.f - Man Page

subroutine zggev3 (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl, ldvl, vr, ldvr, work, lwork, rwork, info)
ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)  

Purpose:

 ZGGEV3 computes for a pair of N-by-N complex nonsymmetric matrices
 (A,B), the generalized eigenvalues, and optionally, the left and/or
 right generalized eigenvectors.

 A generalized eigenvalue for a pair of matrices (A,B) is a scalar
 lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
 singular. It is usually represented as the pair (alpha,beta), as
 there is a reasonable interpretation for beta=0, and even for both
 being zero.

 The right generalized eigenvector v(j) corresponding to the
 generalized eigenvalue lambda(j) of (A,B) satisfies

              A * v(j) = lambda(j) * B * v(j).

 The left generalized eigenvector u(j) corresponding to the
 generalized eigenvalues lambda(j) of (A,B) satisfies

              u(j)**H * A = lambda(j) * u(j)**H * B

 where u(j)**H is the conjugate-transpose of u(j).

Parameters

JOBVL

          JOBVL is CHARACTER*1
          = 'N':  do not compute the left generalized eigenvectors;
          = 'V':  compute the left generalized eigenvectors.

JOBVR

          JOBVR is CHARACTER*1
          = 'N':  do not compute the right generalized eigenvectors;
          = 'V':  compute the right generalized eigenvectors.

N

          N is INTEGER
          The order of the matrices A, B, VL, and VR.  N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA, N)
          On entry, the matrix A in the pair (A,B).
          On exit, A has been overwritten.

LDA

          LDA is INTEGER
          The leading dimension of A.  LDA >= max(1,N).

B

          B is COMPLEX*16 array, dimension (LDB, N)
          On entry, the matrix B in the pair (A,B).
          On exit, B has been overwritten.

LDB

          LDB is INTEGER
          The leading dimension of B.  LDB >= max(1,N).

ALPHA

          ALPHA is COMPLEX*16 array, dimension (N)

BETA

          BETA is COMPLEX*16 array, dimension (N)
          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
          generalized eigenvalues.

          Note: the quotients ALPHA(j)/BETA(j) may easily over- or
          underflow, and BETA(j) may even be zero.  Thus, the user
          should avoid naively computing the ratio alpha/beta.
          However, ALPHA will be always less than and usually
          comparable with norm(A) in magnitude, and BETA always less
          than and usually comparable with norm(B).

VL

          VL is COMPLEX*16 array, dimension (LDVL,N)
          If JOBVL = 'V', the left generalized eigenvectors u(j) are
          stored one after another in the columns of VL, in the same
          order as their eigenvalues.
          Each eigenvector is scaled so the largest component has
          abs(real part) + abs(imag. part) = 1.
          Not referenced if JOBVL = 'N'.

LDVL

          LDVL is INTEGER
          The leading dimension of the matrix VL. LDVL >= 1, and
          if JOBVL = 'V', LDVL >= N.

VR

          VR is COMPLEX*16 array, dimension (LDVR,N)
          If JOBVR = 'V', the right generalized eigenvectors v(j) are
          stored one after another in the columns of VR, in the same
          order as their eigenvalues.
          Each eigenvector is scaled so the largest component has
          abs(real part) + abs(imag. part) = 1.
          Not referenced if JOBVR = 'N'.

LDVR

          LDVR is INTEGER
          The leading dimension of the matrix VR. LDVR >= 1, and
          if JOBVR = 'V', LDVR >= N.

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (8*N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          =1,...,N:
                The QZ iteration failed.  No eigenvectors have been
                calculated, but ALPHA(j) and BETA(j) should be
                correct for j=INFO+1,...,N.
          > N:  =N+1: other then QZ iteration failed in ZHGEQZ,
                =N+2: error return from ZTGEVC.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 214 of file zggev3.f.